SOLUTION: How many whole numbers are there, whose squares and cubes have the same number of digits?

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Question 1126191: How many whole numbers are there, whose squares and cubes have the same number of digits?
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Depends on what you mean by "whole number". Some mathematicians say a whole number is a non-negative integer, some say it is just an integer.


John

My calculator said it, I believe it, that settles it
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
It is clear even without my explanations that for n >= 10 the cube of n,  ,  has MORE digits than  the square  .


Therefore, only 1-digit numbers must be checked

n     n^2     n^3
-----------------

0     0        0    (*)

1     1        1    (*)

2     4        8    (*)

3     9       27

4     16      64    (*)

5     25     125

6     36     256

7     49

8

9

----------------


For your convenience, I marked the favorable numbers by (*), so you can calculate the ANSWER on your own.


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